A005339 Number of ways in which n identical balls can be distributed among 6 boxes in a row such that each pair of adjacent boxes contains at least 4 balls. (Formerly M5245)

35, 154, 424, 930, 1775, 3080, 4985, 7650, 11256, 16006, 22126, 29866, 39501, 51332, 65687, 82922, 103422, 127602, 155908, 188818, 226843, 270528, 320453, 377234, 441524, 514014, 595434, 686554, 788185, 901180, 1026435, 1164890, 1317530

Offset

12,1

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Table of n, a(n) for n=12..44.

D. R. Breach, Letter to N. J. A. Sloane, Jun 1980

Philippe Flajolet, Balls and Urns, etc., A problem in submarine detection (solution to problem 68-16).

M. Hayes (proposer) and D. R. Breach (solver), A combinatorial problem, Problem 68-16, SIAM Rev. 12 (1970), 294-297.

Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 6, -1).

Formula

G.f.: x^12*(35 - 56*x + 25*x^2 - 4*x^3 + x^6)/(1-x)^6. - Vladeta Jovovic, Apr 13 2008

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6), a(12)=35, a(13)=154, a(14)=424, a(15)=930, a(16)=1775, a(17)=3080, a(18)=4985. - Harvey P. Dale, Aug 12 2011

Mathematica

Drop[CoefficientList[Series[x^12(35-56x+25x^2-4x^3+x^6)/(1-x)^6, {x, 0, 60}], x], 12] (* or *) Join[{35}, LinearRecurrence[{6, -15, 20, -15, 6, -1}, {154, 424, 930, 1775, 3080, 4985}, 48]] (* Harvey P. Dale, Aug 12 2011 *)

Crossrefs

Cf. A005337, A005338, A005340.

Sequence in context: A048628 A048629 A133534 * A045614 A154074 A260867

Adjacent sequences: A005336 A005337 A005338 * A005340 A005341 A005342

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Vladeta Jovovic, Apr 13 2008

Name clarified by Alois P. Heinz, Oct 02 2017

Status

approved